In a conventional nuclear magnetic resonance (NMR) experiment, the sample under study is placed in a homogeneous magnetic field produced by a superconducting solenoid. While this facilitates high signal-to-noise (SNR) and spatially resolved magnetic resonance imaging (MRI), it limits the range of samples that can be examined. In recent years, this limitation has been addressed by the introduction of ‘inside out’ or unilateral NMR sensors in which, the fringe field from a permanent magnet array is used to generate the static B0 field in a volume displaced (remote) from the device. A surface coil or an alternate RF probe geometry is used to generate a remote B1 field. The shapes of these inhomogeneous fields define a ‘sensitive volume’ or ‘sensitive spot’ where components of the two fields are orthogonal. Designs of this type allow near surface measurements to be made on samples of arbitrary sizes previously inaccessible to NMR. Furthermore, small permanent magnet designs are easily transported, making them suitable for field applications. The strong gradient inherent in these designs can be exploited to investigate slowly diffusing samples, or to suppress the signal from rapidly diffusing samples.
Inside-out NMR was first used in the oil industry for well logging. Later, Eidmann et al. developed a portable unilateral NMR sensor known as the NMR-MOUSE (see G. Eidmann, R. Savelsberg, P. Blümler, B. Blümich, The NMR MOUSE, a mobile universal surface explorer, J. Magn. Res. A 122 (1996) 104-109). The Eidmann design employs a ‘U’ magnet geometry in which two permanent magnets are arranged on a ferromagnetic yoke in opposite orientations with a gap between them. The B0 field curls between the two magnets, giving a component parallel to their faces in the area over the gap. A surface coil in the gap with its axis normal to the face of the magnets provides the B1 field.
Significant drawbacks exist with the NMR-MOUSE. The B0 field provided by the magnet array is inhomogeneous in all directions and suffers from a strong (10-50 T/m [8]), nonlinear gradient in the direction normal to the array. This results in short signal lifetimes, obscuring chemical shift information and resulting in low SNR measurements. The strong nonlinearity of the gradients results in an ill defined sensitive volume precluding conventional spatially resolved measurements. The strong gradient causes every RF excitation to be slice selective; the size, shape, and position of the excited volume are determined by the bandwidth and frequency of the RF pulse sequence used. These effects limit the effective resolution of the sensor by obscuring the location and distribution of the spin population observed in a measurement. The strong gradient also requires additional RF circuitry to be employed in order to vary the excitation frequency over a wider range in spatially resolved measurements.
To address the drawbacks of early unilateral NMR systems, several designs have been proposed. Using a single bar magnet to provide B0, Blümich et al. developed a unilateral NMR sensor with a small sensitive volume directly over one of the poles of the magnet (see B. Blümich, V. Anferov, S. Anferova, M. Klein, R. Fechete, M. Adams, F. Casanova, Simple NMR-mouse with a bar magnet, Concepts in Magnetic Resonance B 15 (2002) 255-261). In this volume, the gradient parallel to the magnet face is negligible while the gradient normal to the magnet face is strong but approximately linear. While this design offers some advantages in certain applications, the B0 field is orthogonal to the face of the magnet, excluding the use of a simple surface coil to generate B1. Specially designed planar coils must be used, resulting in a decrease in sensitivity.
Many other designs exist wherein the position of magnets in an array is modified in order to achieve some desirable characteristic in the topology of B0. The common feature of these designs is that all deal with a forward problem: given a particular magnet array, determine the resulting B0 field and subsequently determine how this field topology can be applied to achieve experimental goals. There is a need therefore, for an NMR sensor and method to address the inverse problem: given an experimental goal, select an appropriate B0 topology and synthesize a design for an instrument providing this field.
Methods of simulating the B0 field due to a given arrangement of magnets exist. One such example is the Finite Element (FEM) approximation. Designs can be optimized by performing successive simulations while varying parameters to minimize some goal function and this technique has previously been employed in unilateral magnet design. The drawback of this approach is that specific parameters (eg. size, position and strength of magnets) must be selected for the optimization and the parameter space must be empirically selected to suit the desired magnet topology. Furthermore, conventional simulation techniques are computationally expensive, leading to long optimization times, and constraining the number of parameters that can be optimized.
The use of high permeability material is standard in the design of closed permanent magnet NMR systems, where high permeability ‘pole pieces’ are used to control B0 between the magnets. Many methods of shaping the pole pieces to provide an optimal B0 topology have been proposed, however all deal with generating a homogeneous field between two magnets and cannot be directly applied to the unilateral case. Clover et al. have presented a permanent magnet based 1-D profiling system in which pole pieces, shaped according to contours of magnetic scalar potential, were used to give a desired static field (see P. M. Glover, P. S. Aptaker, J. R. Bowler, E. Ciampi, P. J. McDonald, A novel high-gradient permanent magnet for the profiling of planar films and coatings, J. Magn. Res., 139 (1999) 90-97). This approach is attractive in that it offers a low complexity method of configuring magnets and pole pieces to control B0 but the profiling system in Glover et al. is a closed magnet assembly.